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wedrifid comments on The Amanda Knox Test: How an Hour on the Internet Beats a Year in the Courtroom - Less Wrong
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I have also seen Eliezer tempted to consider a '0' probability in response to a 'divide by infinity' situation. (I think there is a 'mathsy' way to represent that kind of '0'.)
That's called a limit. What's special is not the “zero” but the “infinity”: you don't talk about a value “infinity” (attempting to have one causes you to lose various other useful properties), but rather that as some input increases without bound, the output approaches zero.
“The limit of 1/x as x approaches infinity is zero."
The concept of limits is a great way to look at this. A limit is a thing unto its own, a complex statement indicating, confirmed as much as is humanly possible.
Another notion is what Goedel brings to the table. His contribution of something being consistent or complete is relevant.